Recipe from The Romagnolis' Table (1975) -- perhaps my most well worn cookbook. The mushrooms are my own addition. Plus I usually cheat. The Romagnolis instruct one brown the chicken pieces on all sides in oil, thus seasoning the floor and wall. Sometimes I do this (if short on time and I don't mind a few burns on my hands and face).
Better, in my opinion, to cook the chicken parts sous vide. Then dry carefully and brown in the CSO. What I showed in the picture was about 10 minutes on 500C steam broil.
Meanwhile I sautee the mushrooms and garlic (I do like garlic) then add the chicken pieces along with handful of rosemary and a couple bay leaves (since Bugialli's probably not watching). Then to the pan over high heat add lots of white wine vinegar. Let that boil off. Then add white wine. Let that boil down a bit, salt to taste, cover and simmer. (OK, in truth I usually salt when adding the wine vinegar.)
Since by my method the chicken is already fully cooked, the braising time is not critical. I braise for about 20 minutes.
When ready to serve, remove chicken pieces and keep warm.* Add a bit of water to the pan and bring to the boil over high heat. Should make an emulsion. Return the chicken pieces to the pan and serve. If mushrooms are not desired just leave them out. But why would you?
*CSO of course.